Originally proposed by Siegman in his 2003 paper, the concept of gain guiding comes about from the analysis of the V parameter of an optical fiber when the imaginary component of the refractive index is taken into account. The V parameter is the controlling factor in the mode propagation of standard index guiding fibers. Using the V parameter in numerical mode solvers the mode characteristics of an optical fiber or waveguide can be determined. Usually the V parameter is a real number that only takes into account real refractive index. The imaginary component comes about as a result of either loss or gain in the medium that light is propagating through. The V parameter of a waveguide is given by the following equation:
                    V        =                                            2              ⁢              π              ⁢                                                          ⁢              a                        λ                    ⁢                                                                      (                                                            n                      0                                        +                                          Δ                      ⁢                                                                                          ⁢                      n                                                        )                                2                            -                              n                0                2                                                                        (        1        )            where a is the radius of a fiber-core or half width of a slab waveguide, n0 is the cladding index and Δn is the index step between the core and clad. A plane wave propagating in a medium with some gain or loss Δα will propagate according to
  ⅇ            -              j        ⁡                  (                                                    2                ⁢                π                ⁢                                                                  ⁢                z                            λ                        ⁢                          (                                                n                  0                                +                                  Δ                  ⁢                                                                          ⁢                  n                                            )                                )                      +                  Δ        ⁢        a            ⁢                          ⁢      z      the propagation constant in this expression is rewritten as
                                                        2              ⁢                              π                ⁡                                  (                                                            n                      0                                        +                                          Δ                      ⁢                                                                                          ⁢                      n                                                        )                                                      λ                    +                      jΔ            ⁢                                                  ⁢            α                          =                                            2              ⁢                              π                ⁡                                  (                                                            n                      0                                        +                                          Δ                      ⁢                                                                                          ⁢                      n                                        +                                                                  j                        ⁡                                                  (                                                                                    λ                              /                              2                                                        ⁢                            π                                                    )                                                                    ⁢                      Δ                      ⁢                                                                                          ⁢                      α                                                        )                                                      λ                    =                                    2              ⁢                              π                ⁡                                  (                                                            n                      0                                        +                                          Δ                      ⁢                                              n                        ~                                                                              )                                                      λ                                              (        2        )            where ñ is the complex refractive index step which encompasses both index and gain/loss. With this knowledge, the V parameter is rewritten as the complex V-squared parameter to take into account this gain factor.
                                          V            ~                    2                =                                                            (                                                      2                    ⁢                    π                    ⁢                                                                                  ⁢                    a                                    λ                                )                            2                        ⁡                          [                                                                    (                                                                  n                        0                                            +                                              Δ                        ⁢                                                  n                          ~                                                                                      )                                    2                                -                                  n                  0                  2                                            ]                                ≅                                                    (                                                      2                    ⁢                    π                    ⁢                                                                                  ⁢                    a                                    λ                                )                            2                        ⁢            2            ⁢                                          n                0                            ⁡                              (                                                      Δ                    ⁢                                                                                  ⁢                    n                                    +                                      j                    ⁢                                          λ                                              2                        ⁢                        π                                                              ⁢                    Δα                                                  )                                                                        (        3        )            The approximation holds for small index steps and gain. Using numerical mode solving techniques for optical fibers one can use the V-squared parameter to determine the propagation characteristics of modes in an optical fiber which has both gain and index traits. Siegman plots (U.S. Pat. No. 6,751,388) an example of such calculations for the first two modes of a fiber. FIG. 1 is a plot showing the mode boundaries and mode propagation regions for the LP01 and LP11 modes of a cylindrical gain-guiding step-profile in the complex Δn, Δα plane.
As shown in FIG. 1, the propagation of a mode depends upon the value of the index and gain steps. Pure gain guiding can occur in a medium with no index step if the gain term Δα is large enough to support the LP01 mode shown above the first solid line. A combination of negative or positive index difference between core and cladding and a gain or loss step also allows modes to be supported. The Δα axis gives the imaginary part of the V-squared parameter, which can be calculated from the imaginary component of the previous equation. The benefit of gain guiding is that because Δα is fairly small, relatively large cores, which are represented by α in the equation (3), is used and single mode oscillation is maintained. In standard index guided fibers the V parameter is fixed, because it is a function of the refractive index and the core size. In gain guided fibers the gain can be changed to compensate for larger cores regardless of the type of glass material used.
Deficiencies of prior art include the fact that gain guided index antiguided fibers are difficult to pump efficiently, despite a large promise of emitting a single transverse laser mode from a very large core and conventional index guiding large mode area fibers are limited to core sizes of around 25 microns for single mode operation, resulting in a limitation on the possible power produced in the fibers due to high power densities. Even these complex designs have only been proven to be single mode for sizes of <100 micron core sizes. High power non-fiber based lasers like CO2, solid state crystal or thin disk have difficulty reaching high powers and high beam qualities and other large mode area concepts and designs are far more complex and hence expensive to manufacture including Photonic Crystal Fibers or Chirally Coupled Core fibers etc. Currently work on such complex designs has been limited to silica fiber, which may be disadvantageous for some rare earth ions, like Thulium, which require high doping percentages to work efficiently.
Therefore there is a need of finding a solution of the pumping problem in gain guided index antiguided fiber lasers for practical use as a laser gain medium with the gain guided index antiguided fiber designed-to act like a conventional fiber (index guiding) for pump wavelength, and like a gain guided index antiguided fiber (index antiguiding) for signal wavelengths.